February 2026

arXiv:2602.07488v2 Announce Type: replace-cross Abstract: Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token […]

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arXiv:2602.03466v4 Announce Type: replace-cross Abstract: Large language models (LLMs) can generate structured artifacts, but using them as dependable optimizers for scientific design requires a mechanism for iterative improvement under black-box evaluation. Here, we cast quantum circuit synthesis as a closed-loop, test-time optimization problem: an LLM proposes edits to a fixed-length gate list, and an external simulator evaluates the resulting state with the Meyer-Wallach (MW) global entanglement measure. We introduce a lightweight test-time learning recipe that can reuse prior […]

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arXiv:2601.09173v3 Announce Type: replace-cross Abstract: Analysis of learned representations has a blind spot: it focuses on $similarity$, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce $geometric$ $stability$, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present $Shesha$, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated ($rho […]

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arXiv:2510.12026v3 Announce Type: replace-cross Abstract: Mamba, a recently proposed linear-time sequence model, has attracted significant attention for its computational efficiency and strong empirical performance. However, a rigorous theoretical understanding of its underlying mechanisms remains limited. In this work, we provide a theoretical analysis of Mamba’s in-context learning (ICL) capability by focusing on tasks defined by low-dimensional nonlinear target functions. Specifically, we study in-context learning of a single-index model $y approx g_*(langle boldsymbol{beta}, boldsymbol{x} rangle)$, which depends on only […]

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arXiv:2510.08539v3 Announce Type: replace-cross Abstract: Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has found significant empirical success. However, a principled understanding of why it works is lacking. This paper builds a theoretical foundation for RLVR by analyzing its training process at both the full-response (trajectory) and token levels. Central to our analysis is a new quantity called the Gradient Gap, which formalizes the direction of improvement from low-reward to […]

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arXiv:2510.06028v2 Announce Type: replace-cross Abstract: This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The results show that generalization in the low-temperature regime is already signaled by small training errors in the noisier high-temperature regime. The bounds are stable under approximation with Langevin Monte Carlo algorithms. The analysis motivates the design of an […]

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arXiv:2509.05864v2 Announce Type: replace-cross Abstract: In the era of large-scale AI deployment and high-stakes clinical trials, adaptive experimentation faces a “trilemma” of conflicting objectives: minimizing cumulative regret (welfare loss during the experiment), maximizing the estimation accuracy of heterogeneous treatment effects (CATE), and ensuring differential privacy (DP) for participants. Existing literature typically optimizes these metrics in isolation or under restrictive parametric assumptions. In this work, we study the multi-objective design of adaptive experiments in a general non-parametric setting. First, […]

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arXiv:2508.03245v4 Announce Type: replace-cross Abstract: Conformal unlearning aims to ensure that a trained conformal predictor miscovers data points with specific shared characteristics, such as those from a particular label class, associated with a specific user, or belonging to a defined cluster, while maintaining valid coverage on the remaining data. Existing machine unlearning methods, which typically approximate a model retrained from scratch after removing the data to be forgotten, face significant challenges when applied to conformal unlearning. These methods […]

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arXiv:2507.02890v3 Announce Type: replace-cross Abstract: In Industry 4.0 manufacturing environments, forecasting Overall Equipment Efficiency (OEE) is critical for data-driven operational control and predictive maintenance. However, the highly volatile and nonlinear nature of OEE time series–particularly in complex production lines and hydraulic press systems–limits the effectiveness of forecasting. This study proposes a novel informational framework that leverages Topological Data Analysis (TDA) to transform raw OEE data into structured engineering knowledge for production management. The framework models hourly OEE data […]

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arXiv:2501.02624v2 Announce Type: replace-cross Abstract: Approximate Leave-One-Out Cross-Validation (ALO-CV) is a method that has been proposed to estimate the generalization error of a regularized estimator in the high-dimensional regime where dimension and sample size are of the same order, the so-called “proportional regime”. A new analysis is developed to derive the consistency of ALO-CV for non-differentiable regularizers under Gaussian covariates and strong convexity. Using a conditioning argument, the difference between the ALO-CV weights and their counterparts in mean-field […]

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